Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch

The two-degree-of-freedom (2-DOF) airfoil system with freeplay nonlinearity in pitch is investigated numerically. The relation between eigenvalues and flutter speed has been analyzed. The effect of parameters of the freeplay nonlinearity on the system responses is obtained. The probability density function (PDF) and phase plane of the deterministic system have been studied and the results show that the amplitude of limit cycle oscillation (LCO) grows with mean airspeeds increasing. Marginal PDFs, bidimensional PDFs, random bifurcation, and the largest Lyapunov exponent are used in investigation of the random system. The results show that, for low and intermediate level turbulences, the marginal PDFs of system exhibit different characters at different airspeed ranges. However, for high level turbulence the marginal PDFs are similar in the whole airspeed region. The bidimensional PDF has different shapes in low level turbulence at pre- and post-flutter speeds, but the PDF keeps similar shape in high level turbulence. The random bifurcation analysis indicates the P-bifurcation can happen at both pre- and post-flutter speeds but the D-bifurcation never occurs. Numerical simulations approve the results.